In optical communications, many modulation schemes have been used to transport data. On-Off keying (OOK) is one modulation scheme that has been used, where data is encoded using signal intensity variation. OOK introduces strong characteristic tones in the signal frequency domain, which can be detected as periodic intensity variations in the signal. To detect the signals, a conventional clock recovery scheme is used to obtain the timing information in the tones, such as by filtering the detected signal intensities using a narrow band pass filter. Phase Shift Keying (PSK), Differential PSK (DPSK), Quadrature PSK (QPSK), and Differential QPSK (DQPSK) are other modulation schemes that have been used more recently. In such modulation schemes, the data is encoded using signal phase variation. Quadrature phase based modulation has been widely used for many years to achieve high spectrum efficiency in radio frequency (RF) communications systems, including polarization multiplexed optical communications systems. In polarization multiplexed optical communications systems, two signals are carried on one wavelength at two orthogonal linear polarization states, where one signal is modulated in one of the orthogonal polarization states and the other signal is modulated in the other orthogonal polarization state. The quadrature phase modulation in polarization multiplexed optical communications systems can achieve about a four fold improvement in transmission efficiency, e.g. in comparison to other modulation schemes.